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Oak Grove Nail Salon is having a special this month on services. Over the weekend, they performed 16 manicures and 37 pedicures, bringing in a total of $1,043 in receipts. So far this week, they have administered 47 manicures and 36 pedicures, with receipts totalling $1,392. How much does the salon charge for each service?

Respuesta :

absor201

The salon charges $12 for manicure and $23 for pedicure.

Step-by-step explanation:

Let,

x be the charges for each manicure.

y be the charges for each pedicure.

According to given statement;

16x+37y=1043      Eqn 1

47x+36y=1392     Eqn 2

Multiplying Eqn 1 by 47

[tex]47(16x+37y=1043)\\752x+1739y=49021\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 16

[tex]16(47x+36y=1392)\\752x+576y=22272\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 4 from Eqn 3

[tex](752x+1739y)-(752x+576y)=49021-22272\\752x+1739y-752x-576y=26749\\1163y=26749[/tex]

Dividing both sides by 1163

[tex]\frac{1163y}{1163}=\frac{26749}{1163}\\y=23[/tex]

Putting y=23 in Eqn 1

[tex]16x+37(23)=1043\\16x+851=1043\\16x=1043-851\\16x=192[/tex]

Dividing both sides by 16

[tex]\frac{16x}{16}=\frac{192}{16}\\x=12[/tex]

The salon charges $12 for manicure and $23 for pedicure.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/11343416
  • brainly.com/question/11416224

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